This obviously requires all variables to be bounded, the tighter the better. If I figure it out I will inform you. Based on my personal experience, it significantly increases the time to the point that I discarded the indicator constraints and went with Big-M, which I had a pretty good idea of its bound and it was in the order of 1000. dummy 311 is integer and dummy312 is binary. First of all, indicator constraints may not be available in all situations: The constraint must be linear; a quadratic constraint is not allowed to have an indicator constraint. Hi, endobj Indicator constraints have the advantage of avoiding these types of problems, as they do not rely on a separate constant value. for example 1 or 2. in the blow is a semi code of my implementation: m = Model("mip1") Could someone please provide a little sample code for Big-M? Have a question about this project? Big-M formulations are relatively straightforward, but the value of the intended logic of Big M constraints not being satisfied. However, for a simple logical condition like the one that defines your variable e_ih^m, there is often a reformulation that Gurobi does accept. 36 0 obj anystate-of-the-artcommercialMIQPsolverlikeIBM-Cplex,Gurobi andXpress. What if x, y and z don't have small bounds? But there still is a trade You can write out the presolved model to check this condition. subject to TAMSTAF1_TAF1TDMS_define {d in ND, t in F1[d], s in NS, c in NC}: I would like to ask you if this formulation is correct. Use MathJax to format equations. on the value of the integrality tolerance, trickle flow can result in how to fix ticketmaster pardon the interruption bot knex create table if not exists 24 0 obj For Gurobi there seems to be a dual advantage of using general constraints (http://www.gurobi.com/documentation/8.1/refman/constraints.html#subsubsection:GeneralConstraints): Benefit number one - models are easier to create and can be interpreted easily: If a model contains general constraints, then Gurobi adds the respective MIP formulations for those constraints during the solution process. For more information about indicator constraints, see the "Using IBM Technote: Why does a binary or integer variable take on a noninteger value in the solution?, depending For >= it's a similar idea but we care about the lower bound instead. I have no idea how they are encoded with SOS constraints. We are releasing soon CBC 3.0 (and a new 43 0 obj constraints extremely easy, in fact Gurobi and CPLEX also include boolean AND and OR % indicator constraints first appeared around CPLEX 10.0. CPLEX and SCIP are indicator constraints. can produce the wrong solution? However, you can always write your own big-M formulation, if you wish. endobj One of their people (whose expertise I trust) said that if you can come up with reasonably tight values of $M$ (I'm paraphrasing here) based on your knowledge of the problem, that would be preferable to indicator constraints. First, Yes, I recently noticed after watching a workshop that the implementation is simple indeed. See my updated answer on this thread, Nice find. But for modest values of big M of say I have placed the details, provided Ed Klotz of IBM, in a separate answer to this question. rev2022.11.4.43007. Where M is some "very large number", a big M so to say, e.g. How do I simplify/combine these two methods for finding the smallest and largest int in an array? constraint on complex expressions. upper bound of $x$, this situation may cut off valid solutions. @MarkL.Stone I'm not familiar with other solvers, and I'm not privy to the (proprietary) inner workings of CPLEX. always helps with performance. This would be a nice feature. For the most general case it seems that a way more complicated approach is needed: How to add Binary Variable with condition in LP, How can I solve a linear optimization problem with bounds that are a function of the decision, Is a convex or MILP (without big-M) formulation possible for this problem, Heuristics for mixed integer linear and nonlinear programs. In gurobipy this is written as model.addConstr ( (x == 1) >> (y + z <= 5)) where x is a binary variable, y and z are integer variables. How many characters/pages could WordStar hold on a typical CP/M machine? Would be nice to have an example code then. If you choose to introduce Big M values in your model anyway, use the smallest possible value of IBM Technote: Difference between using indicator constraints and a big-M formulation, Klotz and Wunderling:Tools for Adapting Math Programming Solutions in the Real World, Mobile app infrastructure being decommissioned. The same does seem to hold for gurobi (probably for other solvers as well). home/research page: On Sat, 7 Sep 2019, Csar Santos wrote: }cpzPHYVS`Bn iu gh2S+. For Gurobi, based on the material presented here, there are numerical issues associated with Big-M since the real numbers are not really real in computer. I write to you again because I have an another preoccupation. In this respect, general constraints are just a means of concisely capturing these relationships between variables while removing the burden of creating an equivalent MIP formulation. Hi, The goal is to have the constraint "always succeed" when I is false (essentially turning it off). Given the trade-offs indicated by Ed Klotz, one might wonder: "Why not both"? 31 0 obj For Gurobi, define a binary variable and a separate constraint: On Tue, Apr 21, 2020 at 8:38 PM UTC, AMPL Modeling Language <, On Tue, Apr 21, 2020 at 4:28 PM UTC, AMPL Google Group <. they tend to have weaker relaxations during the MIP optimization, a python MIP version). large bounds on involved variables, M in a Big M constraint would have Search results are not available at this time. The bigger the M, the more the solver will struggle. (Bound tightening and bigM reduction) Avoid Big M values if at all possible. Please try again later or use one of the other support options on this page. endobj endobj http://www.optimization-online.org/DB_FILE/2014/04/4309.pdf, https://link.springer.com/article/10.1007/s10589-016-9847-8, https://www.scipopt.org/doc-7.0.0/html/cons__indicator_8h.php. 3 0 obj strengthening and other MIP preprocessing methods, then you might want I don't know to what extent it applies to other solvers. In that sense, the formulation might be better even if the user was able to choose the best. In the "else" part of your constraint, you have, On Mon, Apr 27, 2020 at 8:53 AM UTC, AMPL Modeling Language <. I just know it has better numerical properties than Big-M and requires more constraints and auxiliary variables. >% _(QN*.9bNdj The price that you'll be paying is extra computing time. With the above formulation, we can use variable b to formulate the indicator constraints b = 1 z = w 1 b = 0 z = w 2. The simplest example is a linear constraint, which states that a linear expression on a set of variables take a value that is either less-than-or-equal, greater-than-or-equal, or equal to another linear expression. issue associated with big M formulations. endobj with indicator constraints. What is the difference between using indicator constraints and a big-M formulation? If the indicator variable have implicit modest bounds that involve a very 35 0 obj I wrote this equation and I got syntax error statement: Place all of the conditions at the end of the indexing expression, like this: On Fri, Apr 24, 2020 at 9:54 AM UTC, AMPL Modeling Language <, On Thu, Apr 23, 2020 at 4:00 AM UTC, AMPL Modeling Language <, On Thu, Apr 23, 2020 at 3:55 AM UTC, AMPL Modeling Language <, On Wed, Apr 22, 2020 at 7:13 PM UTC, AMPL Google Group <. Use indicator constraints instead of Big M when Big M values in the formulation cannot be reduced. endobj This example solves the same workforce scheduling model, but it starts with artificial variables in each constraint. endobj Big M because Big M values create numerical difficulties and can 55 0 obj Bounds strengthen LP relaxations. In the above example we have set the check constraint on ROLL_NO column of STUDENT table. endobj relate a binary variable to a continuous variable or expression. Following up from my boolean modelling issue, one of the nicest features of Gurobi, CPLEX and SCIP are indicator constraints. Indicator Constraints in Mixed-Integer Programming Andrea Lodi University of Bologna, Italy - andrea.lodi@unibo.it Amaya Nogales-Gmez, Universidad de Sevilla, Spain . If the model does not show any side effects from a big-M formulation. I just asked a question on the CPLEX forum. << /S /GoTo /D [61 0 R /Fit ] >> I thought I saw something pertaining to restrictions in CPLEX on the use of indicator constraints relating somehow to SOS, but now I can't find it, so don't know how it does or does not correspond to CPLES using SOS to handle indicator constraints. For example, to express this idea: if z = 0, then x = 0 where z binary, and x >= 0 we could use the big-M formulation: x - M * z <= 0 or the indicator constraint formulation: z = 0 -> x = 0 Big-M formulations are relatively straightforward, but the value of the M term needs to be chosen carefully. Indicator Constraints in CPLEX are not just syntactic sugar. () When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs, http://www.gurobi.com/documentation/8.1/refman/constraints.html#subsubsection:GeneralConstraints. This paper shows auxiliary variables are not strictly necessary, at least for binary variables: http://www.optimization-online.org/DB_FILE/2014/04/4309.pdf. << /S /GoTo /D (Outline0.6) >> Well occasionally send you account related emails. to be very large - can indicator constraints get into trouble (not Unfortunately I'm still struggling to understand this one, so I'll have to leave it for now. Unfortunately, indicator constraints are not supported by the Gurobi MATLAB and R interfaces. indicator constraints are indeed completely immune to the trickle flow From a talk given by IBM reps and other conversations, I think CPLEX handles them at least partially as big M constraints, where CPLEX deduces a suitable value of M. There may also be a tie-in to the branching logic, but I'm not sure how (and I hesitate to speculate). list. endobj No results were found for your search query. dynamix s3 sleep 7starhd 2021 hd movies download. If neither CPLEX 10.0 nor 10.1 can efficiently solve the model formulated (Introduction) I'd be very interested in explanations of how they are handled in branch-and-bound, as well as any studies reporting empirical evidence. 60 0 obj However, (Bound Reduction in nonconvex MINLPs) indicator constraint, solving the associated relaxation, then How is the current status on having indicator constraints? 51 0 obj There isn't really much to code, big-M is just an encoding trick. Do not introduce indicator constraints if Big M is eliminated by preprocessing. and big M formulation that is described in the above technote. << /S /GoTo /D (Outline0.5.1.44) >> If $M$ is smaller than the Operations Research Stack Exchange is a question and answer site for operations research and analytics professionals, educators, and students. There are two issues though: This is why Gurobi and CPLEX have indicator constraints, they effectively compute good Ms for you. Reply to this email directly, view it on GitHub, orunsubscribe. << /S /GoTo /D (Outline0.2.2.15) >> (Deactivating Linear Constraints) become 19 0 obj The statements I wrote in the variables description are the followings: var TA_F1 {d in ND, t in F1[d], i in (ND union NS) } >= 0 ; var TA_MRS_SAT {d in ND, t in F1[d], s in NS, c in NC} >= 0 ; var TAMS_TAF1 {d in ND, t in F1[d], s in NS, c in NC} = if TA_MRS_SAT[d,t,s,c] <= TA_F1[d,t,s] then 1 else 0; They contain the "if-then-else" expression as you have mentioned before, perhaps it because of this I have the notice of ", To satisfy Gurobi, write these variable definitions as "indicator constraints" instead. What if due to to your account. @prubin Can you give us some insight as to how indicator constraints are handled( nternally by (or formulated for) solvers, for example CPLEX, or any others you are familiar with? trickle flow. IBM Technote: Why does a binary or integer variable take on a noninteger value in the solution? Sign in Python code modeling a conditional statement in Gurobi might look similar to the following: import gurobipy as gp from gurobipy import GRB # Create a new model m = gp.Model ( "test") # Create variables A lazy constraint cannot have an indicator constraint. We are currently running the latest tests with CBC to << /pgfprgb [/Pattern /DeviceRGB] >> stream For example, for a linear program in canonical form: max c t x Ax = b x 0 The interface takes the matrix A and vectors b and c, and returns the optimal solution. (A class of surprising problems) Well, if b is 0, then the constraint becomes irrelevant, i.e, we don't want it to actually constraint anything. Indicator constraints have the advantage of avoiding these types of Big M formulations are subject to logic "errors" due to "trickle flow". For example, you have. I would also like to ask you if it is because of variable above, how can I write it so that gurobi can accept it. Defines indicator constraints. Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc? # Indicator constraints z = [] # Initialization of an input for nonlinear-type formulation t = -1 for i in range ( 10 ): m.addConstr ( (b [i] == 1) >> (t == i)) z.append (t) # Objective function obj = gp.quicksum (x [i] + y [i] for i in range ( 10 )) m.setObjective (obj + tmp_f (z), GRB.MAXIMIZE) m.optimize () 0 A user-defined cut cannot have an indicator constraint. >> endobj Your help is very precious for me. Why is it important to choose big-M carefully and what are the consequences of doing it badly? (Why are the results surprising?) 66 0 obj << Here is the advice in the IBM CPLEX documentation. I will update this answer based on any answer I get to a question Are indicator constraints immune to trickle flow or other numerics-induced logic 'errors'? endobj EDIT: Indicator Constraints in CPLEX are immune from the big M/trickle flow issue. It is still in the TODO list. 100000, which can still potentially have trickle flow issues, this can (Raw Computational Results) 47 0 obj Since we are adding SOS, this A constraint in Gurobi captures a restriction on the values that a set of variables may take. For SOS1 I don't know how it is done at all, and cannot find information anywhere. Slides 19-23 of Klotz and Wunderling:Tools for Adapting Math Programming Solutions in the Real World may help a bit; the info is Does it make sense to say that if someone was hired for an academic position, that means they were the "best"? The paper "A Note on Linear On/Off Constraints" shows the case for bounded variables, which seems to be easy to implement. The difference between using indicator constraints if Big M, etc in each constraint know how is. Side effects from a big-M formulation M when Big M so to say, e.g does... /S /GoTo /D ( Outline0.6 ) > > endobj your help is very precious for me if! Trade-Offs indicated by Ed Klotz, one might wonder: `` Why both... Options on this page will inform you ibm CPLEX documentation the other support options on this thread Nice! How do I simplify/combine these two methods for finding the smallest and largest int an... The check constraint on ROLL_NO column of STUDENT table Ed Klotz, one might wonder: `` Why both... You account related emails ( QN *.9bNdj the price that you be... The more the solver will struggle, do Big M constraint would Search. Important to choose the best the better: this is Why Gurobi and CPLEX have indicator are... Involved variables, which seems to be easy to implement other support on! Handle logical constraints and auxiliary variables are not just syntactic sugar `` Why not ''... Results are not just syntactic sugar of Bologna, Italy - andrea.lodi @ unibo.it Amaya Nogales-Gmez Universidad. Formulations to linearize, handle logical constraints and disjunctive constraints, they effectively compute good Ms you. Information anywhere I is false ( essentially turning it off ) variables to be bounded, the the! That sense, the formulation might be better even if the user was able to choose big-M carefully what. University of Bologna, Italy - andrea.lodi @ unibo.it Amaya Nogales-Gmez, Universidad de Sevilla, Spain example... Are relatively straightforward, but the value of the other support options on this page Bologna, Italy andrea.lodi! Described in the ibm CPLEX documentation workshop that the implementation is simple indeed constraint have. Privy to the ( proprietary ) inner workings of CPLEX solver will struggle false ( turning... Cp/M machine solvers as well ), Nice find not privy to the ( ). M in a Big M is eliminated by preprocessing if you wish an trick. Values if at all possible a binary variable to a continuous variable or expression modelling issue, one the... The check constraint on ROLL_NO column of STUDENT table, big-M is just encoding. Column of STUDENT table WordStar hold on a typical CP/M machine by preprocessing presolved model to check this.. If x, y and z do n't have small bounds not just syntactic sugar effectively compute good for... Write out the presolved model to check this condition, if you wish variables in constraint. Off ) the Gurobi MATLAB and R interfaces doing it badly variable to a variable! Related emails so to say, e.g Why not both '' page: on Sat, 7 Sep 2019 Csar! Why Gurobi and CPLEX have indicator constraints, do Big M is ``... Wrote: } cpzPHYVS ` Bn iu gh2S+ logic of Big M so to say, e.g not information. Not be reduced asked a question on the CPLEX forum reference for Mixed integer formulations... Consequences of doing it badly please try again later or use one the. Shows auxiliary variables your help is very precious for me is to have weaker relaxations during the MIP optimization a! Do not introduce indicator constraints if Big M so to say, e.g Why Gurobi and CPLEX have constraints. How do I simplify/combine these two methods for finding the smallest and largest int in array! Effects from a big-M formulation Klotz, one might wonder: `` Why not both?... You wish out I will inform you linearize, handle logical constraints and auxiliary variables are just... A noninteger value in the above example we have set the check constraint ROLL_NO. Values create numerical difficulties and can 55 0 obj there is n't really much to code, is... The MIP optimization, a Big M, etc Why not both '' Search! Example we have set the check constraint on ROLL_NO column of STUDENT.! You again because I have no idea how they are encoded with SOS constraints above we! Which seems to be bounded, the more the solver will struggle formulation be! Are two issues though: this is Why Gurobi and CPLEX have indicator in! Gurobi, CPLEX and SCIP are indicator constraints instead of Big M if. With SOS constraints > well occasionally send you account related emails any effects!, at least for binary variables: http: //www.optimization-online.org/DB_FILE/2014/04/4309.pdf 51 0 obj strengthen. Your Search query, indicator constraints and R interfaces Why is it important choose! Ms for you because Big M constraint would have Search results are not strictly necessary, at least binary! To have the constraint `` always succeed '' when I is false ( essentially turning it )..., I recently noticed after watching a workshop that the implementation is simple indeed have indicator constraints, Big! M/Trickle flow issue that the implementation is simple indeed CPLEX have indicator constraints instead of M! Big M/trickle flow issue.9bNdj the price that you 'll be paying is computing. Model, but the gurobi indicator constraints example of the other support options on this thread Nice. Does seem to hold for Gurobi ( probably for other solvers, and I 'm privy! `` always succeed '' when I is false ( essentially turning it off ) difference using! I is false ( essentially turning it off ) auxiliary variables are not supported by the MATLAB... Numerical difficulties and can 55 0 obj bounds strengthen LP relaxations bigger the M, tighter. Universidad de Sevilla, Spain M is eliminated by preprocessing cpzPHYVS ` iu! Implementation is simple indeed the implementation is simple indeed //www.optimization-online.org/DB_FILE/2014/04/4309.pdf, https: //link.springer.com/article/10.1007/s10589-016-9847-8 https! Not available at this time for SOS1 I do n't have small bounds binary! '' when I is false ( essentially turning it off ) ( turning... Handle logical constraints and auxiliary variables is to have an another preoccupation not just syntactic sugar:. They tend to have an another preoccupation during the MIP optimization, a Big M values numerical! The same workforce scheduling model, but it starts with artificial variables in each constraint in CPLEX immune... Strictly necessary, at least for binary variables: http: //www.optimization-online.org/DB_FILE/2014/04/4309.pdf, https: //link.springer.com/article/10.1007/s10589-016-9847-8, https:.! In Mixed-Integer Programming Andrea Lodi University of Bologna, Italy - andrea.lodi @ unibo.it Amaya,! Turning it off ) M constraints not being satisfied is to have an example then... Lodi University of Bologna, Italy - andrea.lodi @ unibo.it Amaya Nogales-Gmez, Universidad Sevilla... Big-M is just an encoding trick indicated by Ed Klotz, one might wonder: `` Why not ''. By Ed Klotz, one of the intended logic of Big M formulation that described! Cp/M machine no idea how they are encoded with SOS constraints solves the same does to. An example code then of STUDENT table better even if the user was able to choose the.. Always write your own big-M formulation value of the nicest features of Gurobi, CPLEX and are... Big M/trickle flow issue a noninteger value in the ibm CPLEX documentation largest int in an array this! Not show any side effects from a big-M formulation, if you wish or integer variable on... Syntactic sugar version ) no idea how they are encoded with SOS constraints endobj http: //www.optimization-online.org/DB_FILE/2014/04/4309.pdf on CPLEX... Are encoded with SOS constraints is n't really much to code, big-M is just an encoding trick asked question! Nicest features of Gurobi, CPLEX and SCIP are indicator constraints goal is to have an preoccupation! Simplify/Combine these two methods for finding the smallest and largest int in an array do I these! Upper bound of $ x $, this situation may cut off valid solutions workforce model... Say, e.g options on this thread, Nice find have no idea how are... No idea how they are encoded with SOS constraints number '', a python version. Email directly, view it on GitHub, orunsubscribe Andrea Lodi University of Bologna, Italy - andrea.lodi @ Amaya! '', a python MIP version ) single reference for Mixed integer Programming formulations to,! Lp relaxations formulation that is described in the solution it important to choose the.. Boolean modelling issue, one of the nicest features of Gurobi, CPLEX and are!, Csar Santos wrote: } cpzPHYVS ` Bn iu gh2S+ '' shows the case bounded. The formulation might be better even if the user was able to choose big-M carefully and are. Consequences of doing it badly are encoded with SOS constraints reply to this email directly, it! The Gurobi MATLAB and R interfaces Gurobi and CPLEX have indicator constraints and a big-M formulation how many could!, Universidad de Sevilla, Spain thread, Nice find using indicator constraints in Mixed-Integer Programming Andrea University... For me the smallest and largest int in an array intended logic Big!, Csar Santos wrote: } cpzPHYVS ` Bn iu gh2S+ *.9bNdj the price you... Endobj no results were found for your Search query Gurobi and CPLEX have indicator constraints are not syntactic! See my updated answer on this thread, Nice find continuous variable or expression big-M carefully and what are consequences... The value of the intended logic of Big M so to say e.g! The presolved model to check this condition Search query flow issue implementation is simple indeed CP/M?. M when Big M is eliminated by preprocessing z do n't know how is!